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But before that, lawmakers face an immediate transportation-funding shortfall.

The House committee tasked with shaping the next generation of highways is trying to make sure they're ready for the next generation of cars—including ones without drivers.

The House Transportation and Infrastructure panel is trying to forge a long-term transportation bill, which sets policy and funding for the nation's roads and transit agencies. Panel Chairman Bill Shuster said Tuesday that the measure will include a new section on technology aimed at addressing driverless cars and other in-development forms of transportation.

"These cars are coming," the Pennsylvania Republican said at a National Journal LIVE event Tuesday. "When we build a road in the next five to ten years, it's going to have a driverless vehicle on it sometime in the near future."

Lawmakers face challenges in designing roads that can accommodate such vehicles, everything from broad planning to specifics, such as what road and paint materials the next-gen cars could "sense" as they operate.

Shuster said he's talking to representatives from technology companies and the House Energy and Commerce Committee about how to start accounting for the new technology in a transportation bill. Elsewhere, Carnegie-Mellon University in Pittsburgh is working on a three-year study of autonomous cars.

Before it addresses far-off technology, however, Congress faces a near-immediate transportation funding cliff. Congress only has until the end of May—33 days from Tuesday—before the current surface-transportation bill expires and states lose federal transportation funds.

Shuster said he's working with the Ways and Means Committee to find the roughly $10 billion that Congress would need to fund a short-term bill. Although the length will depend on what sort of budget tricks Ways and Means can come up with, Shuster said he's pushing for a five- or six-month bill to get states through construction season.

Sen. Jim Inhofe, who heads the Senate Environment and Public Works Committee and oversees transportation in that chamber, has called for an extension to the end of the fiscal year on September 30, but Shuster said the extension should go longer.

He declined to say what options were available for the short term bill, simply saying, "It's tough." But with the deadline looming and the House on recess next week and later in May for Memorial Day, Shuster said he'll try to move the patch in the next few weeks.

Looking ahead to the long-term bill later this year, Shuster said he anticipated a bill that would last five or six years, enough to provide certainty to the construction industry and states to start working on multiyear projects.

He said that he's "nudging Paul Ryan the best I can" to get the Ways and Means chairman to free up more money for the bill, adding he's confident funding levels will be "at least the same levels." He conceded that there wasn't a long-term fix on the table at the moment, but "that has to be job one" when a bill gets passed.

"Going around the country and giving people the choice between more money and a shorter-term bill, or about the same money and a long-term bill, it's unanimous," Shuster said. "Everyone wants that five or six years of certainty."

The Highway Trust Fund is fueled by the 18.4-cents-per-gallon gas tax, but it hasn't been raised or indexed to inflation since 1993. That has left the transportation fund on the brink of collapse; the Transportation Department has said it could be bankrupt by the end of August.

Shuster said that a gas-tax increase is likely off the table, given opposition from leaders in both parties and the White House.

"I'm for what's possible, and I don't think at this point that's possible," Shuster said. "I do believe that after we get this done and the president signs a five-year bill, stakeholders and members of Congress that care about it have to really start figuring out, ... How do we fund this?"